(Covers information from Both Timelines)
Hurley's Camaro was a Chevrolet Camaro (ca. 1970–1972) that originally belonged to his father, David Reyes. When David left his family in 1987, the Camaro remained in Hurley's possession. ("Tricia Tanaka Is Dead") After returning from the Island, Hurley drove the car during a car chase with the police, ending in a crash. ("The Beginning of the End")
Before Hurley's time on the Island
In 1987, David Reyes and his son were trying to fix the broken car, but to no avail. They came to the conclusion that it needed a new carburetor. David told his son that they had to postpone their work on the car because he had to leave for Las Vegas. Subsequently, he would leave his family for 17 years. ("Tricia Tanaka Is Dead")
In 2004, following Hurley's lottery win, David Reyes returned to his family at the request of his wife, trying to talk Hurley out of his belief that his lottery numbers were cursed. To his surprise, he found out that Hurley had kept the car for 17 years, still in the same state it had been when he had left his family. David tried to talk Hurley into trying to fix the car again, but instead, Hurley decided to leave for Australia. ("Tricia Tanaka Is Dead")
After Hurley's time on the Island
David began work on the Camaro some time after the crash, as a tribute to Hurley. After the rescue, David gave the Camaro to Hurley for his birthday. Hurley got in, and freaked out when he saw that the odometer read "481516 - 2342", saying that he didn't want it. ("There's No Place Like Home, Part 1"). Some time later, following a run-in with what he believed to be the ghost of Charlie Pace, he fled in the car, resulting in a car chase with the police. The chase began at the convenience store where he had had the vision. The chase continued into an industrial area where he drove it through a stack of papayas.
The chase then continued onto a freeway where it was filmed by a helicopter television news crew from Action 8 News, and broadcast live, where Jack observed it while having a drink. The car chase ended near a "Circuit House" store parking lot with the Camaro becoming airborne and subsequently crashing into a Golden Pontiac, followed by Hurley's arrest by the police. This final sequence was filmed by his former boss and employee Randy Nations, who was working at the Circuit House. ("The Beginning of the End") The Camaro was back in the garage at Hurley's house when Hurley's father took a sedated Sayid to Jack for help. ("The Lie")
Bloopers and continuity errors
The Camaros used in both "Tricia Tanaka Is Dead" and "The Beginning of the End" appear to very consistent with each other (if not the same car); however, the Camaro used in "There's No Place Like Home, Part 1" is clearly different. The most notable differences are the front bumper, grill, front parking/turn lamp locations, rear traction-bars, rear trunk spoiler, and the white stripes near the top edge of the grill. The Camaro used in "There's No Place Like Home, Part 1" appears to be a genuine Z28, while the other Camaro(s) seems to be your average run-of-the-mill backyard special. The Camaro in "The Beginning of the End" has a ‘Z28’ badge on the rear trunk spoiler, but a larger spoiler than the Camaro in "There's No Place Like Home, Part 1".
The change in cars could be due to the fact that the original Camaro was damaged in the chase & crash scene in "The Beginning of the End", so a replacement Camaro had to be found; that’s assuming that the episodes were shot in order and that the same Camaro was used in both episodes. The 'newly restored' Camaro first appears in "There's No Place Like Home, Part 1", which chronologically takes place between the other two episodes in the Lost Timeline, where the other Camaro(s) appears.